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lfunc_lfunctions • Show schema
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{'Lhash': '496208218504572591453452252941', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0.6420736324815003], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 3.5877414504720115], 'a8': [0, 0], 'a9': [2.5877414504720115, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.34315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.3649', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '1982259441850717304180760960337', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.6420736324815003], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.5877414504720115], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 1.3579263675184998], [-13.0, 0]], [[1.0, 0], [0, -5.587741450472011], [-17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 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'3.69165310339962767369560678963634', '4.28796108798481282090230690788040', '5.02279608309189650407825623625427', '6.15247918805716268122484083626149', '6.87942598608891239478802721835397', '7.53182315848715269852763828934625', '7.74432118609443604928201055271160'], 'prelabel': '2-3800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': -0.42620819117478337, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39143926442762275536399869671', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41903135605133277498661569868', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.45743926949288468244277081776', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.34315276808656, 'bad_primes': [2, 5, 19], 'central_character': '5.4', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/d/l/3649/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3800-5.4-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39143926442762275536399869671', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '496208218504572591453452252941', 'Lhash_array': ['496208218504572591453452252941'], 'factors': ['2-3800-5.4-c1-0-13'], 'label': '2-3800-5.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/d/l/3649/4'}